What equation is used in R ccf and Julia crosscor?
I scratch my head a lot. Now, except for the fact that Julia gives a seemingly opposite result in relation to delays
julia> crosscor([1,2,3,4], [1,2,3,1])'
1x7 Array{Float64,2}:
-0.30339 0.0 0.64049 0.13484 -0.37081 -0.40452 0.30339
> print(ccf(c(1,2,3,4), c(1,2,3,1), type="correlation", plot=F))
Autocorrelations of series ‘X’, by lag
-3 -2 -1 0 1 2 3
0.303 -0.405 -0.371 0.135 0.640 0.000 -0.303
which is easily solved by reversing x and y ("easy" relative, when it takes an hour of your life to figure out), the numbers are unlike any of the equations I'm familiar with (which anyway).
So, I opened my statistics textbook and found many other formulas that I am not going to test with pen and paper. I suspected for a moment that removing funds from vectors played a role, so I didn't try to do this (unfortunately, this can only be done in Julia)
julia> crosscor([1,2,3,4], [1,2,3,1], demean=false)'
1x7 Array{Float64,2}:
0.188562 0.518545 0.942809 0.848528 0.518545 0.235702 0.0471405
but that still doesn't look like the normalized cross-correlation that I calculated with pen and paper (pending mistakes I could make).
In short: I need to cite a formula, so what is it?
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I'm guessing quoting this excerpt here is ok with StackOverflow terms of use? On page 390 (section 14.1) of Venables and Ripley (2002), you can find the definition they use here for a function acf()
:
If you look at the source code for the function ccf()
in R (enter "ccf" at the prompt), you can see how it is used acf()
, and you can ask how the above implementation acf()
relates to calculation.
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